# Semiparametric model averaging for high-dimensional quantile regression with nonignorable nonresponse

## TL;DR

This paper introduces a novel semiparametric model averaging approach for high-dimensional quantile regression with nonignorable missing data, improving model selection and estimation accuracy in incomplete datasets.

## Contribution

It develops a semiparametric model averaging method that handles nonignorable missingness and asymptotically concentrates on the correct model, advancing quantile regression techniques.

## Key findings

- The proposed SMA estimator achieves asymptotic optimality.
- The method effectively handles complex missingness mechanisms.
- Empirical results demonstrate improved efficiency over existing methods.

## Abstract

Model averaging has demonstrated superior performance for ensemble forecasting in high-dimensional framework, its extension to incomplete datasets remains a critical but underexplored challenge. Moreover, identifying the parsimonious model through averaging procedure in quantile regression demands urgent methodological innovation. In this paper, we propose a novel model averaging method for high-dimensional quantile regression with nonignorable missingness. The idea is to relax the parametric constraint on the conditional distribution of respondents, which is constructed through the two-phase scheme: (i) a semiparametric likelihood-based estimation for the missing mechanism, and (ii) a semiparametric weighting procedure to combine candidate models. One of pivotal advantages is our SMA estimator can asymptotically concentrate on the optimally correct model when the candidate set involves at least one correct model. Theoretical results show that the estimator achieves asymptotic optimality even under complex missingness conditions. Empirical conclusions illustrate the efficiency of the method.